If 2x^2 - 3x - m is divisible by (x - 3) what is m?

Essentially we need to factor 2x^2 -3x -m and they tell us one of the factors is (x - 3)

When we're factoring picture doing FOIL in reverse. So if one of the first terms is x then the other would need to be 2x so that their product is 2x^2. So at this point we have it factored as

(x - 3) (2x___)

We also know the outer and inner term would need to have a sum of -3x. And with what we have factored the inner terms would have a product of - 6x (-3*2x). So the outer terms have to have a product of 3x. For the outer terms to have a product of 3x, the missing number would have to be 3, so it would factor to

(x - 3)(2x + 3)

Now multiply these to get

2x^2 -3x - 9

So we know m = 9 and D is correct.

While you could also plug in values for x, in this case you would likely need to try a few different numbers to narrow the answer choices down to one, so algebra is more efficient on this one.

Take care,
Sionainn